To understand ourselves is to reflect on time. But to to understand time, we need to reflect on ourselves.
-Carlo Rovelli, The Order of Time
I remember A Brief History of Time by the late Stephen Hawking was among the first popular science books I read. However, I ended up wondering why he named his book as a history of time instead of a history of the universe in time. Not until many years later, I found another book containing a glorious and poetic attempt to explore the origin of time. That book is The Order of Time by Carlo Rovelli. He divided the book into three parts: the first part talks about modern physics understanding of time that points toward its elusive nature, the second part talks about a universe without time, and lastly, he explored how could time emerges from a timeless universe. In this post, I will focus on the first and the last parts.
Time in fundamental physics
Time is absolute, according to Newton. He thinks of time as a universal tick-tock throughout the entire universe, always flowing with the same rate and it is independent of any observer or physical events. In Newtonian physics, space and time are immovable backstages behind every event in the universe. His thought was very influential and unquestionable before young Albert Einstein challenged his assumption with special and general relativity.
Einstein, following the path carved by Maxwell, showed that time flows differently depending on how fast an object is moving relative to each other, and later, relative to the strength of gravity in the area. Objects that move faster or under stronger gravitational influence experience slower time. Space and time, no longer act as a stage but plunge themselves into the play.
If the flow of time is object-dependent, how can then we define the present? Since the present for one observer might be the past for another. As an example, consider the question “what is the present state of Proxima B?”. Proxima B is 5 light-years away from us. Because any information about the state of Proxima B can not travel faster than light, the most accurate description we can possibly get about Proxima B is its state 5 years ago. But, it does not answer our question since we are interested in the present state of Proxima B, not its state 5 years ago. Perhaps, the present state of Proxima B is the state that will be observed 5 years from now. This does not work either for 5 years from now, the definition of “the present” has already changed.
The fact is that relativity demolishes the notion of “universal present”. There is no single moment at Proxima B that corresponds to the present here on earth. The notion of time as a singular quantity without any reference to location becomes meaningless. In other words, one can not talk about time without talking about space. This is where the notion of spacetime emerges.
With regards to the flow of time, Einstein famously said the following:
“The distinction between the past, the present, and the future is only a stubbornly persistent illusion.”
To be fair, Einstein wasn’t talking about science when he said this. He was attending a funeral for his lifelong friend. However, it is also true that for people who are working on fundamental physics, time seems to not appear in the fundamental equations. That is, the law of the universe does not seem to distinguish the past and the future. To illustrate, consider a recording of two billiard balls colliding with each other. One can talk about the conservation of momentum and energy with regards to this event, but one can not say whether the recording was played forward or backward. It makes no difference, both of them are plausible according to the laws of mechanics.
The only fundamental equation that distinguishes the past and the future is the second law of thermodynamics, which says that in a closed system, entropy always increases with time. For example, if we see a video of eggs falling from a height and breaking into small pieces, it is easy enough to distinguish forward recording and the reversed one. Why? Because in the forward recording entropy increases while it decreases in the reversed recording.
But what the hell is entropy? And why would it keep increasing?
The Relativity of Entropy
S = k log W
A simple equation carved on Boltzmann’s tomb, a soft-hearted genius who unfortunately ended his own life. Boltzmann showed that entropy- initially interpreted only as a practical quantity for heat engine calculation- has a fundamental meaning. It means precisely the number of possible states a system can have without making any difference to our observation. Consider a set of blackjack cards. Let’s assume that the deck is arranged in such a way that all the red cards are on top and the black cards are on the bottom. The entropy of the cards is the number of ways this configuration can be realized. For instance, you can choose between the king of heart or ace of diamond as the topmost card. As far as the color is concerned, the red ones are still on top and the black ones are on the bottom no matter which one you choose.
However, note that the two configurations are the same because we pay attention to the colors. If we pay attention to other aspects of the cards, say the symbols (heart, diamond, clubs, spades), your choice would matter. Entropy then depends on what information you pay attention to and what you ignore. Let’s call this factor as the “blurring” factor since blurring means ignoring some information contained in the system. The same configuration can have a low entropy according to one blurring factor and a high entropy according to another. If you pay attention to every little detail (zero blurrings) of the system, all configurations would have equal entropy and thus the concept of entropy is no longer useful.
Is entropy subjective then? It is not. Science as a discipline pursues objectivity. If entropy is subjective, it would not be useful to define it as a scientific concept.
Entropy, like time, is a relative quantity. The entropy of A with regards to a blurring factor B counts the number of configurations of A that the interaction between A and B does not distinguish.
Now, that we have discussed what entropy is, shall we move on to why does it always increase?
Does the universe have a watch?
In fact, photons don’t experience any time at all. … From the perspective of a photon, there is no such thing as time. It’s emitted, and might exist for hundreds of trillions of years, but for the photon, there’s zero time elapsed between when it’s emitted and when it’s absorbed again
We have seen previously how entropy is a relative quantity, it depends on the interaction between the system and its environments. All of this finally lead to the big idea narrated nicely in Rovelli’s The Order of Time.
What if the reason entropy always increases (and thus fixing the order of time) is due to the way we as a living system interact with the universe?
In this way, the order of time has more to do with ourselves than the universe itself. Perhaps it is due to our brains constantly anticipating stimulus from the environment based on our past memories. There are billions of objects in the universe, and the notion of time might be meaningless to them since they do not interact with the universe the way we do.
It’s a radical idea, far from being commonly accepted by the scientific community. The alternative is to accept the universe started in a low entropy configuration and its increasing flow emerges due to the influence of Big Bang. Just like the concept of up and down emerges from earth’s gravity (in free space, there is no inherent sense of direction), the flow of time emerges from Big Bang’s singularity, whatever happened at that moment.
So, does the universe have a watch? If Rovelli is correct, probably not.